Although I can't speak yet as-to the technical support times for AWS (I'm mid-migration to there right now!), I do know from experience that any technical support you need on MS Azure will take a long time. Unless you pay (quite a bit of money!) for a monthly support contract in addition to your cloud server cost, any ticket you open up with them will be of low-priority, meaning you'll be waiting for a few hours at minimum for a response, let alone any action. They also have no phone number to call. Just about every ticket we ever opened with them were due to technical glitches in their stack, so that didn't help much either.
Rackspace is better for this, they do have a phone number and will respond fairly quickly in general. I still found their support greatly lacking, but at least they would answer the phone or get back to you.
Digital Ocean I've heard is quite good. I've had a small server there for a couple years, and never had any problems where I needed to contact support, so I really don't know what it's like in terms of support. However, if you need the more advanced functionality you get with AWS/MS Azure/RS, you're not going to find it with them.
The whole cloud industry's technical and customer service in my opinion is a race to the bottom; a competition to see who can be the least-worst provider. If you're making a decision on behalf of a company requiring considerable infrastructure, you are likely best off getting a DevOps provider to handle all the messy technical support stuff.